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bekas [8.4K]
2 years ago
12

If a multiple-choice test consists of 5 questions, each with 4 possible answers of which only 1 is correct, (a) in how many diff

erent ways can a student check off one answer to each question?
(b) in how many ways can a student check off one answer to each question and get all the answers wrong?
Mathematics
1 answer:
Papessa [141]2 years ago
5 0

Answer:

  (a)  1024 ways

  (b)  243 ways

Step-by-step explanation:

When answers are independent, the total number of ways all questions can be answered is the product of the number of ways each question can be answered.

__

<h3>(a)</h3>

The first question can have one answer 4 ways. The second question can be answered 4 ways for each of the ways the first question was answered. That is, the two questions can be answered 4×4 = 16 ways. Similarly, each additional question multiplies the number of ways the questions can be answered by 4.

The 5 questions can be answered 4×4×4×4×4 = 4^5 = 1024 ways.

__

<h3>(b)</h3>

There are 3 ways to answer the first question incorrectly. Each additional question can be answered incorrectly 3 ways for each of the ways previous questions were answered. The total number of ways all questions can be answered incorrectly is ...

  3^5 = 243

A student can answer all questions wrong in 243 different ways.

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Answer:

$2.20

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Divide the $5 by 11.

11 divided by 11 is 1.

So 1 pound of rice is $2.20.

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If f(x)=3x-2 and g(x)=x^2+1, find f(g(-1)) and g(f(3))
julsineya [31]

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Step-by-step explanation:

We know the definition of both functions: f(x)=3x-2, and g(x)=x^2+1

A) In order to evaluate what f(g(-1)) is, let's first investigate what g(-1) is using the definition for this function:

g(x)=x^2+1\\g(-1)=(-1)^2+1\\g(-1)=1+1\\g(-1)=2

Now let's find what f(2) is using f(x) definition: f(x)=3x-2\\f(2)=3(2)-2\\f(2)=6-2\\f(2)=4

B) In order to evaluate what g(f(3)) is, let's first investigate what f(3) is using the definition for this function:

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Now let's find what g(7) is using the definition for this function:

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